It's doubtful that Jesus healed people on the Sabbath just to tweak the noses of the Jewish authorities, but he certainly did not shy away from healing on the Sabbath in their presence. The healing of the man with the shriveled hand is told amidst a series of stories where Jesus confronts the religious leaders. The account in Luke 6:6-11 specifically tells us that Jesus knew that they were watching him to see what he would do and even knew what they were thinking. So when Jesus asks them, "Which is lawful on the Sabbath: to do good or to do evil, to save life or to destroy it?" they can't deny that he has them pegged.
But there is a second reason they can't answer. Jesus has framed the question differently than they would have. To them, the issue was that Jesus was practicing his profession (healing) on the Sabbath which was forbidden. But Jesus puts his healing in terms of good and evil. They could hardly reply that it was forbidden to do good on the Sabbath.
For Reflection: There are often many ways to approach an issue, a question, a problem. Do I seek out the opinions of others on what approach to take? The counsel of someone wiser in the ways of God can be of tremendous benefit.
I started this website and blog on May 1, 2012. I am a Catholic who has been in ministry for many years. I first developed what I would call a close relationship with Jesus in the early 1970s. Ever since then I have been praying with people for healing and other needs. It is because I have seen so many of these prayers answered that I am so bold as to offer to pray for you individually through this website and phone line.